A MULTISCALE MODELING SCHEME BASED ON PERIDYNAMIC THEORY
R Rahman and JT Foster and A Hague, INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING, 12, 223-248 (2014).
In this paper a multiscale modeling framework has been established between peridynamics (PD) and atomistic models. Typically, atomistic models are governed by molecular dynamics schemes (MD). Both PD and MD formulations are nonlocal. The atomistic model is coupled with a PD- based continuum model through a hierarchical multiscale modeling framework. In this framework, PD models at higher length scale act as an external environment for the PD models at a smaller length scale. Based on a similar idea, a smaller length scale PD model is seamlessly linked with the atomistic model. At the end of this hierarchical downscaling, information such as displacement field, deformation, etc. were captured in the atomistic region. The updated atomistic model is interconnected with all the PD models in the length scale hierarchy. This multiscale modeling scheme is named as "PFHMM: A peridynamics-based framework for hierarchical multiscale modeling." In this paper the mathematical formulation of PFHMM is discussed rigorously. Also, a thorough mathematical analysis is carried out in order to show that the issue with wave reflection between different models at different length scales is absent in PFHMM. The proposed multiscale modeling scheme is illustrated for different cases. It is seen that the displacement field has a strong correlation with the length scale of the material. Such an observation was verified with the experimental observation (i.e., example 4 on nanoindentation).
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